ART: adaptive residual--time restarting for Krylov subspace matrix\n exponential evaluations

2018/12/25 by M.A. Botchev, Botchev, Mikhail A., Leonid Knizhnerman +1 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #35Q61 #65F30 #65F60 #65L05 #65N22 #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1812.10165

openalex publication_date 2018/12/25 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

In this paper a new restarting method for Krylov subspace matrix exponential\nevaluations is proposed. Since our restarting technique essentially employs the\nresidual, some convergence results for the residual are given. We also discuss\nhow the restart length can be adjusted after each restart cycle, which leads to\nan adaptive restarting procedure. Numerical tests are presented to compare our\nrestarting with three other restarting methods. Some of the algorithms\ndescribed in this paper are a part of the Octave/Matlab package expmARPACK\navailable at http://team.kiam.ru/botchev/expm/.\n

Cited by

• Randomized orthogonalization and Krylov subspace methods: principles and algorithms
• A general framework for Krylov ODE residuals with applications to randomized Krylov methods

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